Is there a way to learn someone's level in game in DnD3.x?Hmmm... It sounds like you are looking more for something within your world, rather than a rules based thing. Maybe you could implement some form of official magic ranking system, in which people need to achieve some form of goal to advance in? This really doesn't sound like something you'd need the rules for, specifically.

Looking for a game that does not need anything but character sheetsYou might want to look into some old text-based RPG, as they didn't rely on visual aides and were interacted with purely through text. These also were less combat focused and more about puzzle/problem solving. The combat systems varied heavily from very intricate combat to very basic (one-two hit kill, maybe needs a specific weapon), so you might be able to mimic a less random-intensive system.